Exploring Expressions Involving a Non-Zero Real Number

For a real number $x \neq 0$, it is given that

Determine all values of:
a) $x - \frac{1}{x}$
b) $x + \frac{1}{x}$
c) $\left( x + \frac{1}{x} \right)^2$
d) $x^3 - \frac{1}{x^3}$